Answer :
Answer:
Step-by-step explanation:
To multiply the polynomial \(5a^2b - 3ab^2 + 4ab - 7\) by \(3a^2b\), we distribute \(3a^2b\) to each term in the polynomial.
Given polynomial: \(5a^2b - 3ab^2 + 4ab - 7\)
Multiplier: \(3a^2b\)
### Step-by-Step Multiplication:
1. **Multiply \(5a^2b\) by \(3a^2b\):**
\[
5a^2b \cdot 3a^2b = 5 \cdot 3 \cdot a^{2+2} \cdot b^{1+1} = 15a^4b^2
\]
2. **Multiply \(-3ab^2\) by \(3a^2b\):**
\[
-3ab^2 \cdot 3a^2b = -3 \cdot 3 \cdot a^{1+2} \cdot b^{2+1} = -9a^3b^3
\]
3. **Multiply \(4ab\) by \(3a^2b\):**
\[
4ab \cdot 3a^2b = 4 \cdot 3 \cdot a^{1+2} \cdot b^{1+1} = 12a^3b^2
\]
4. **Multiply \(-7\) by \(3a^2b\):**
\[
-7 \cdot 3a^2b = -7 \cdot 3 \cdot a^2 \cdot b = -21a^2b
\]
### Combine All the Results:
\[
15a^4b^2 - 9a^3b^3 + 12a^3b^2 - 21a^2b
\]
Thus, the result of multiplying \(5a^2b - 3ab^2 + 4ab - 7\) by \(3a^2b\) is:
\[
15a^4b^2 - 9a^3b^3 + 12a^3b^2 - 21a^2b
\]